In recent years the Markov Random Field (MRF) has
become the de facto probabilistic model for low-level vision
applications. However, in a maximum a posteriori
(MAP) framework, MRFs inherently encourage delta function
marginal statistics. By contrast, many low-level vision
problems have heavy tailed marginal statistics, making the
MRF model unsuitable. In this paper we introduce a more
general Marginal Probability Field (MPF), of which the
MRF is a special, linear case, and show that convex energy
MPFs can be used to encourage arbitrary marginal
statistics. We introduce a flexible, extensible framework
for effectively optimizing the resulting NP-hard MAP problem,
based around dual-decomposition and a modified mincost
flow algorithm, and which achieves global optimality
in some instances. We use a range of applications, including
image denoising and texture synthesis, to demonstrate
the benefits of this class of MPF over MRFs.
Oliver J. Woodford, Carsten Rother, Vladimir Kolmo